 
Summary: PROCESS SYSTEMS ENGINEERING
Global Optimization of MixedInteger Nonlinear
Problems
C. S. Adjiman, I. P. Androulakis, and C. A. Floudas
Dept. of Chemical Engineering, Princeton University, Princeton, NJ 08544
Two no容l deterministic global optimization algorithms for noncon容x mixedinteger
( )problems MINLPs are proposed, using the ad家nces of the BB algorithm for non
con容x NLPs of Adjiman et al. The special structure mixedinteger BB algorithm
( )SMIN BB addresses problems with noncon容xities in the continuous 家riables and
linear and mixedbilinear participation of the binary 家riables. The general structure
( )mixedinteger BB algorithm GMIN BB is applicable to a 容ry general class of
problems for which the continuous relaxation is twice continuously differentiable. Both
algorithms are de容loped using the concepts of branchandbound, but they differ in
their approach to each of the required steps. The SMIN BB algorithm is based on the
con容x underestimation of the continuous functions, while the GMIN BB algorithm
is centered around the con容x relaxation of the entire problem. Both algorithms rely on
optimization or inter家lbased 家riablebound updates to enhance efficiency. A series of
mediumsize engineering applications demonstrates the performance of the algorithms.
Finally, a comparison of the two algorithms on the same problems highlights the 家lue
of algorithms that can handle binary or integer 家riables without reformulation.
